Key Equations

speed of sound

v = f λ

Doppler effect observed frequency (moving source)	$f_{o b s} = f_{s} (\frac{v_{w}}{v_{w} \pm v_{s}})$
Doppler effect observed frequency (moving observer)	$f_{o b s} = f_{s} (\frac{v_{w} \pm v_{o b s}}{v_{w}})$

beat frequency	$f_{B} = \| f_{1} - f_{2} \|$
resonant frequencies of a closed-pipe resonator	$f_{n} = n \frac{v}{4 L}, n = 1, 3, 5...$
resonant frequencies of an open-pipe resonator	$f_{n} = n \frac{v}{2 L}, n = 1, 2, 3...$

Resources